Related papers: On the thermodynamic limit for a one-dimensional s…
We obtain analytic expressions for the time correlation functions of a liquid of spherical particles, exact in the limit of high dimensions $d$. The derivation is long but straightforward: a dynamic virial expansion for which only the first…
The divisible sandpile starts with i.i.d. random variables ("masses") at the vertices of an infinite, vertex-transitive graph, and redistributes mass by a local toppling rule in an attempt to make all masses at most 1. The process…
A particular type of random dynamical processes is considered, in which the stochasticity is introduced through randomly fluctuating parameters. A method of local multipliers is developed for treating the local stability of such dynamical…
In this paper, we show that the Gibbs measure of the stochastic hyperbolic sine-Gordon equation on the circle is the unique invariant measure for the Markov process. Moreover, the Markov transition probabilities converge exponentially fast…
We analyze mean-field equations obtained for models motivated by a large station-based car-sharing system in France called Autolib. The main focus is on a version where users reserve a parking space when they take a car. In a first model,…
An exact reduced dynamical map along with its operator sum representation is derived for a central spin interacting with a thermal spin environment. The dynamics of the central spin shows high sustainability of quantum traits such as…
This work concerns random dynamics of hyperbolic entire and meromorphic functions of finite order and whose derivative satisfies some growth condition at infinity. This class contains most of the classical families of transcendental…
It is argued that a Gibbsian formula for the space-time distribution of microscopic trajectories of a nonequilibrium system provides a unifying framework for recent results on the fluctuations of the entropy production. The variable entropy…
In analogy to Brownian computers we explicitly show how to construct stochastic models, which mimic the behaviour of a general purpose computer (a Turing machine). Our models are discrete state systems obeying a Markovian master equation,…
We construct a mean field theory for the lattice model of a structural glass and solve it using the replica method and one step replica symmetry breaking ansatz; this theory becomes exact in the limit of infinite dimensions. Analyzing…
We study the thermodynamical properties of a one-dimensional gas with one-dimensional gravitational interactions, and placed in a uniform mass background. Periodic boundary conditions are implemented as a modification of the potential…
As a fundamental thermodynamic principle, speed limits reveal the lower bound of entropy production (EP) required for a system to transition from a given initial state to a final state. While various speed limits have been developed for…
The Buridan's ass paradox is characterized by perpetual indecision between two states, which are never attained. When this problem is formulated as a dynamical system, indecision is modeled by a discrete-state Markov process determined by…
Consider an N-dimensional Markov chain obtained from N one-dimensional random walks by Doob h-transform with the q-Vandermonde determinant. We prove that as N becomes large, these Markov chains converge to an infinite-dimensional Feller…
It is now well established that there is no lower bound for the energy dissipated during a computation. The relevance of the zero-energy limit is unclear, however, because it entails computations that are unreliable or infinitely slow, or…
This paper investigates the limit behavior of Markov Decision Processes (MDPs) made of independent particles evolving in a common environment, when the number of particles goes to infinity. In the finite horizon case or with a discounted…
A covariant way to define the relativistic entropy of a finite object has been proposed. The energy-momentum of an object with finite volume is not a covariant physical entity because of the relativity of simultaneity. A way to correctly…
Local thermal equilibrium generally implies the absence of heat flux within a fluid. We find the relations between a set of thermodynamic variables of a fluid on a general spacetime and those defined on a conformally connected spacetime,…
Developing a thermodynamic theory of computation is a challenging task at the interface of non-equilibrium thermodynamics and computer science. In particular, this task requires dealing with difficulties such as stochastic halting times,…
By considering general Markov stochastic dynamics and its coarse-graining, we study the framework of stochastic thermodynamics for the original and reduced descriptions corresponding to different scales. We are especially concerned with the…